Stability margins of nonlinear optimal regulators with nonquadratic performance criteria involving cross-weighting terms

In this paper we derive guaranteed gain, sector, and disk margins for nonlinear optimal and inverse optimal regulators that minimize a nonlinear-nonquadratic performance criterion involving cross-weighting terms. Specifically, sufficient conditions that guarantee gain, sector, and disk margins are given in terms of the state, control, and cross-weighting nonlinear-nonquadratic weighting functions. The proposed results provide a transparent generalization of the "meaningful" inverse optimal nonlinear regulator stability margins as well as the classical linear-quadratic optimal regulator gain and phase margins.